Thursday, 26 August 2010

Mother Nature's Scaffold

A preview of a track which is almost completed- inspired by swinging one's head towards the clouds and seeing local workers scale dizzying heights on bamboo skeletons, shrouding entire buildings at a time. This is for the bamboo architects...

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In Schwarzschild coordinates, the Schwarzschild metric has the form:
c^2 {d \tau}^{2} = \left(1 - \frac{r_s}{r} \right) c^2 dt^2 - \frac{dr^2}{1-\frac{r_s}{r}} - r^2 \left(d\theta^2 + \sin^2\theta \, d\varphi^2\right)
where
τ is the proper time (time measured by a clock moving with the particle) in seconds,
c is the speed of light in meters per second,
t is the time coordinate (measured by a stationary clock at infinity) in seconds,
r is the radial coordinate (circumference of a circle centered on the star divided by 2π) in meters,
θ is the colatitude (angle from North) in radians,
φ is the longitude in radians, and
rs is the Schwarzschild radius (in meters) of the massive body, which is related to its mass M by
r_{s} = \frac{2GM}{c^{2}}
where G is the gravitational constant.[1]